54 lines
2.1 KiB
Mathematica
54 lines
2.1 KiB
Mathematica
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%%*****************************************************************
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%% NTscaling: Compute NT scaling matrix
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%%
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%% compute SVD of Xchol*Zchol via eigenvalue decompostion of
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%% Zchol * X * Zchol' = V * diag(sv2) * V'.
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%% compute W satisfying W*Z*W = X.
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%% W = G'*G, where G = diag(sqrt(sv)) * (invZchol*V)'
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%% important to keep W symmertic.
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [W,G,sv,gamx,gamz,dd,ee,ff] = ...
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NTscaling(blk,X,Z,Zchol,invZchol);
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numblk = size(blk,1);
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W = cell(numblk,1); G = cell(numblk,1); sv = cell(numblk,1);
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gamx = cell(numblk,1); gamz = cell(numblk,1);
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dd = cell(numblk,1); ee = cell(numblk,1); ff = cell(numblk,1);
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%%
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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numblk = length(pblk{2});
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n = sum(pblk{2});
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if strcmp(pblk{1},'l')
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dd{p} = X{p}./Z{p}; %% do not add perturbation, it badly affects cre-a
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elseif strcmp(pblk{1},'q');
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gamx{p} = sqrt(qops(pblk,X{p},X{p},2));
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gamz{p} = sqrt(qops(pblk,Z{p},Z{p},2));
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w2 = gamz{p}./gamx{p}; w = sqrt(w2);
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dd{p} = qops(pblk,1./w2,ones(n,1),4);
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tt = qops(pblk,1./w,Z{p},3) - qops(pblk,w,X{p},4);
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gamtt = sqrt(qops(pblk,tt,tt,2));
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ff{p} = qops(pblk,1./gamtt,tt,3);
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ee{p} = qops(pblk,sqrt(2)./w,ff{p},4);
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elseif strcmp(pblk{1},'s')
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tmp = Prod2(pblk,Zchol{p},X{p},0);
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tmp = Prod2(pblk,tmp,Zchol{p}',1);
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[sv2,V] = blkeig(pblk,tmp);
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sv2 = max(1e-20,sv2);
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sv{p} = sqrt(sv2);
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tmp = Prod2(pblk,invZchol{p},V);
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G{p} = Prod2(pblk,spdiags(sqrt(sv{p}),0,n,n),tmp');
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W{p} = Prod2(pblk,G{p}',G{p},1);
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end
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end
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%%**********************************************************************
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